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If we reject a hypothesized value because it differs from the sample statistic by more than...

If we reject a hypothesized value because it differs from the sample statistic by more than 1.75 standard errors, what is the probability that we have rejected a hypothesis that is actually true?

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Answer #1

Answer: probability = 0.0401

Explanation:

A Type I error is defined as the probability of rejecting the null hypothesis when the null hypothesis is actually TRUE”. In a statistical test analysis, it is defined as the p-value (or the observed significance level).

The hypothesized value differs from the sample statistic by more than 1.75 standard errors which means the standardized test statistic (z statistic) of the test is 1.75

The p-value for the z statistic is obtained from the z distribution table for z = 1.75 (In excel use function =1-NORM.S.DIST(1.75,TRUE))

P-value = 0.040059

Hence there is approximately 4% chance that the null hypothesis is rejected when the null hypothesis is actually TRUE

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